9,358 research outputs found
Deterministic Annealing and Nonlinear Assignment
For combinatorial optimization problems that can be formulated as Ising or
Potts spin systems, the Mean Field (MF) approximation yields a versatile and
simple ANN heuristic, Deterministic Annealing. For assignment problems the
situation is more complex -- the natural analog of the MF approximation lacks
the simplicity present in the Potts and Ising cases. In this article the
difficulties associated with this issue are investigated, and the options for
solving them discussed. Improvements to existing Potts-based MF-inspired
heuristics are suggested, and the possibilities for defining a proper
variational approach are scrutinized.Comment: 15 pages, 3 figure
Reactive Planar Manipulation with Convex Hybrid MPC
This paper presents a reactive controller for planar manipulation tasks that
leverages machine learning to achieve real-time performance. The approach is
based on a Model Predictive Control (MPC) formulation, where the goal is to
find an optimal sequence of robot motions to achieve a desired object motion.
Due to the multiple contact modes associated with frictional interactions, the
resulting optimization program suffers from combinatorial complexity when
tasked with determining the optimal sequence of modes.
To overcome this difficulty, we formulate the search for the optimal mode
sequences offline, separately from the search for optimal control inputs
online. Using tools from machine learning, this leads to a convex hybrid MPC
program that can be solved in real-time. We validate our algorithm on a planar
manipulation experimental setup where results show that the convex hybrid MPC
formulation with learned modes achieves good closed-loop performance on a
trajectory tracking problem
Conic Optimization Theory: Convexification Techniques and Numerical Algorithms
Optimization is at the core of control theory and appears in several areas of
this field, such as optimal control, distributed control, system
identification, robust control, state estimation, model predictive control and
dynamic programming. The recent advances in various topics of modern
optimization have also been revamping the area of machine learning. Motivated
by the crucial role of optimization theory in the design, analysis, control and
operation of real-world systems, this tutorial paper offers a detailed overview
of some major advances in this area, namely conic optimization and its emerging
applications. First, we discuss the importance of conic optimization in
different areas. Then, we explain seminal results on the design of hierarchies
of convex relaxations for a wide range of nonconvex problems. Finally, we study
different numerical algorithms for large-scale conic optimization problems.Comment: 18 page
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